半导体材料与技术课件：chapter3-7（第一章）.ppt

1、Chapter 3 Semiconductors3.1 Intrinsic semiconductors3.2 Extrinsic semiconductors3.3 Temperature dependence of conductivity3.4 Schottky junction and Ohmic contactsFrom Principles of electronic Materials Devices, SO Kasap (McGraw-Hill, 2005)3.1 Intrinsic semiconductors3.1.1 Silicon crystal and energy

2、band diagram-Intrinsic semiconductor: undoped semiconductor, is a pure semiconductor without any significant dopant species present. -The number of charge carriers is therefore determined by the properties of the material itself instead of the amount of impurities. -In intrinsic semiconductors the n

3、umber of excited electrons and the number of holes are equal: n = p.3.1 Intrinsic semiconductors3.1.1 Silicon crystal and energy band diagramSilicon Crystal StructureElectronic configuration of an isolated Si atom: Ne 3s2p2（四面体）3.1 Intrinsic semiconductors3.1.1 Silicon crystal and energy band diagra

4、mSeen in Fig. (a), simplified two dimensional illustration of a Si atom with four hyb. Each hyb orbital has one electron so that they are half-occupied. (a)Therefore, a hyb orbital of one Si atom can overlap a hyb orbital of a neighbouring Si atom to form a covalent bond (B) with two spin-paired ele

5、ctrons.3.1 Intrinsic semiconductors3.1.1 Silicon crystal and energy band diagramIn this manner, one Si atom bonds with four other Si atoms by overlapping the half-occupied hyb orbitals, illustrated in Fig. (b); then Neighboring Si atoms can form covalent bonds with other Si atoms; thus form a three-

6、dimentional network of Si atoms.Si crystal structure 3.1 Intrinsic semiconductors3.1.1 Silicon crystal and energy band diagram(1) VB contains those electronic states that correspond to the overlap of bonding orbitals (B).(2) VB is full with the valence electrons since all B are full with them.(c) Th

7、e energy band diagram of Si crystal at absolute zero of temperature.3.1 Intrinsic semiconductors3.1.1 Silicon crystal and energy band diagram(3) CB contains electronic states with higher energies, corresponding to overlapping of antibonding orbitals. (4) CB is separated from VB by an energy gap (Eg)

8、, called bandgap. (c) The energy band diagram of Si crystal at absolute zero of temperature.3.1 Intrinsic semiconductors3.1.1 Silicon crystal and energy band diagramEg = energy gap (bandgap); Ev = top of the VB; Ec = bottom of the CB = electron affinity=energy distance from Ec to vaccum level=width

9、of the CB;(c) The energy band diagram of Si crystal at absolute zero of temperature.3.1 Intrinsic semiconductors3.1.1 Silicon crystal and energy band diagramNotice:(1) The electrons in VB of Fig. (c) are those in the covalent bonds between the Si atoms in Fig. (b). (2) Electron in VB is not localize

10、d to an atomic site but extends throughout the whole solid.3.1 Intrinsic semiconductors3.1.1 Silicon crystal and energy band diagramNotice:(3)Although the electrons appear localized in Fig. (b) at the bonding orbitals between the Si atoms, actually, in crystal, electrons can tunnel from one bond to

11、another and exchange places. The electrons in the covalent bonds are indistinguishable. We cant label an electron from the start and say that the electron is in the covalent bond between these two atoms.(Heisenbergs uncertainty principle)Crudely represent: a two dimensional pictorial view of the Si

12、crystal showing covalent bonds as two lines where each line is a valence electron.3.1.2 Electrons and holes-The only empty electronic states in Si are in CB. An electron placed in CB is free to move around the crystal and respond when applied electric field because there are plenty of neighbouring e

13、mpty energy levels. -An electron in CB can easily gain energy from the field and move to higher energy levels because these states are empty. -Generally we can treat an electron in CB as if it were free in the crystal with certain modifications to its mass. 3.1.2 Electrons and holes(a) A photon with

14、 an energy greater than Eg can excite an electron from the VB to the CB. (b) When a photon breaks a Si-Si bond, a free electron and a hole in the Si-Si bond is created.3.1.2 Electrons and holesSince the only empty states are in CB, the excitation of an electron from VB requires a minimum energy of E

15、g.The electron absorbs the incident photon and gains sufficient energy to surmount the energy gap Eg and reach the CB. 3.1.2 Electrons and holesConsequently, a free electron and a hole, corresponding to a missing electron in VB, are created.In some semiconductors: Si and Ge, the photon absorption pr

16、ocess also involves lattice vibrations (vibrations of Si atoms), not shown in Fig. (b).Thermal vibrations of atoms can break bonds and thereby create electron-hole pairs.Except the specific example of a photon (hEg) creating an electron-hole pair, there is another electron-hole generation process go

17、ing on: thermal generation.Due to thermal energy, the atoms in the crystal are constantly vibrating, which corresponds to the bonds between the Si atoms being periodically deformed. Thermal vibrations of atoms can break bonds and thereby create electron-hole pairs.In a certain region, the atoms, at

18、some instant, may be moving in such a way that a bond becomes overstretched, seen below. This will result in the overstretched bond rupturing and hence releasing an electron into CB (the electron effectively becomes free). The empty electronic state of the missing electron in the bond is what we cal

19、l a hole in the valence band. A pictorial illustration of a hole in the valence band wandering around the crystal due to the tunnelling of electrons from neighbouring bonds.The free electron in CB, can wander around the crystal and contribute to the electrical conduction when applied an electric fie

20、ld. The region remaining around the hole in VB is positively charged because a charge of e has been removed from an other wise neutral region of the crystal. A pictorial illustration of a hole in the valence band wandering around the crystal due to the tunnelling of electrons from neighbouring bonds

21、.This hole, denoted as h+, can also wander around the crystal as if it were free. This is because an electron in a neighbouring bond can jump/tunnel into the hole to fill the vacant electronic state at this site and thereby create a hole at its original position. This is effectively equivalent to th

22、e hole being displaced in the opposite direction, seen in Fig. (a) A pictorial illustration of a hole in the valence band wandering around the crystal due to the tunnelling of electrons from neighbouring bonds.This single step can reoccur, causing the hole to be further displaced.As a result, the ho

23、le moves around the crystal as if it were a free positively charged entity, in Fig. (a) to (d). When applied an electric field, the hole will drift in the direction of the field and hence contribute to electrical conduction. A pictorial illustration of a hole in the valence band wandering around the

24、 crystal due to the tunnelling of electrons from neighbouring bonds.There are two types of charge carriers in semiconductors: electrons and holes. A hole is effectively an empty electronic state in VB that behaves as if it were a positively charged particle free to respond to an applied electric fie

25、ld. A pictorial illustration of a hole in the valence band wandering around the crystal due to the tunnelling of electrons from neighbouring bonds.Recombination: when a wandering electron in CB meets a hole in VB, the electron has found an empty state of lower energy and therefore occupies the hole.

26、 The electron falls from CB to VB to fill the hole, seen Fig. (e) and (f). This results in the annihilation of an electron in CB and a hole in VB. A pictorial illustration of a hole in the valence band wandering around the crystal due to the tunnelling of electrons from neighbouring bonds.The excess

27、 energy of the electron falling from CB to VB is emitted as a photon, as GaAs and InP.In Si and Ge, the excess energy is lost as lattice vibration (heat).Notice: electron has a wavefunction in the crystal that is extend not localized as in Figure below. We cannot localize the hole to a particular si

28、te as well. 3.1.3 Conduction in semiconductorsAfter applied an electric field across a semiconductor, the energy bands bend.When an electric field is applied, electrons in the CB and holes in the VB can drift and contribute to the conductivity. (a) A simplified illustration of drift in Ex. (b) Appli

29、ed field bends the energy bands since the electrostatic PE of the electron is -eV(x) and V(x) decreases in the direction of Ex whereas PE increases.3.1.3 Conduction in semiconductorsThe total electron energy E is KE+PE, but now there is an additional electrostatic PE contribution. A uniform electric

30、 field Ex implies a linearly decreasing potential V(x), by virtue of (dV/dx)=-Ex, that is , V=-Ax+B. So, PE, eV(x), of the electron is now eAx-eB, which increases linearly across the sample. Therefore, all the energy levels (energy bands) must tilt up in the x direction, shown below. When an electri

31、c field is applied, electrons in the CB and holes in the VB can drift and contribute to the conductivity. (a) A simplified illustration of drift in Ex. (b) Applied field bends the energy bands since the electrostatic PE of the electron is -eV(x) and V(x) decreases in the direction of Ex whereas PE i

32、ncreases.3.1.3 Conduction in semiconductorsThe drift of the electron in applied field, as in Fig. (a): Under Ex, the electron in CB moves to the left and immediately starts gaining energy from the field. When the electron collides with a thermal vibration of a Si atom, it loses some of this energy a

33、nd thus falls down in energy in CB. After the collision, the electron starts to accelerate again, until the next collision, and so on. When an electric field is applied, electrons in the CB and holes in the VB can drift and contribute to the conductivity. (a) A simplified illustration of drift in Ex

34、. (b) Applied field bends the energy bands since the electrostatic PE of the electron is -eV(x) and V(x) decreases in the direction of Ex whereas PE increases.3.1.3 Conduction in semiconductorsThe drift velocity vde of the electron is eEx where e is the drift mobility of the electron. The drift of t

35、he hole in applied field: the drift is along the field. When a hole gains energy, it moves down in VB because the potential energy of the hole is of opposite sign to that of the electron.When an electric field is applied, electrons in the CB and holes in the VB can drift and contribute to the conduc

36、tivity. (a) A simplified illustration of drift in Ex. (b) Applied field bends the energy bands since the electrostatic PE of the electron is -eV(x) and V(x) decreases in the direction of Ex whereas PE increases.3.1.3 Conduction in semiconductorsSince both electrons and holes contribute to electrical

37、 conduction, we may write the current density J, from its definition, asJ = envde + epvdhWhere n is the electron concentration in CB, p is the hole concentration in VB, and vde and vdh are the drift velocities of electrons and holes in response to an applied electric field Ex, Thus, vde = e Ex and v

38、dh = h ExWhere e and h are the electron and hole drift mobilities. When an electric field is applied, electrons in the CB and holes in the VB can drift and contribute to the conductivity. (a) A simplified illustration of drift in Ex. (b) Applied field bends the energy bands since the electrostatic P

39、E of the electron is -eV(x) and V(x) decreases in the direction of Ex whereas PE increases.3.1.3 Conduction in semiconductors3.1.3 Conduction in semiconductors3.1.3 Conduction in semiconductors3.1.3 Conduction in semiconductorsA hole has a mass?YES! As long as we view mass as resistance to accelerat

40、ion, there is no reason why the hole should not have a mass. Accelerating the hole means accelerating electrons tunneling from bond to bond in the opposite direction. Therefore the hole will have a nonzero finite inertial mass because otherwise the smallest external force will impart an infinite acc

41、eleration to it. 3.1.3 Conduction in semiconductors3.1.4. Electron and hole concentration(a) Energy band diagram. (b)Density of states (number of states per unit energy per unit volume). (c) Fermi-Dirac probability function (probability of occupancy of a state). (d) The product of g(E) and f(E) is t

42、he energy density of electrons in the CB (number of electrons per unit energy per unit volume). The area under nE(E) vs. E is the electron concentration in the conduction band.The general equation for the conductivity of a semiconductor (=ene+ eph) depends on n and p. How to determine them?We define

43、 gcb(E) as the density of states in CB, the number of states per unit energy per unit volume. We know that the probability of finding an electron in a state with energy E is given by the Fermi-Dirac function f(E). The gcb(E)f(E) is the actual number of electrons per unit energy per unit volume nE(E)

44、 in CB. Thus,nE dE = gcb(E) f(E) dEis the number of electrons in the energy range E to E+dE. 3.1.4. Electron and hole concentration(a) Energy band diagram. (b)Density of states (number of states per unit energy per unit volume). (c) Fermi-Dirac probability function (probability of occupancy of a sta

45、te). (d) The product of g(E) and f(E) is the energy density of electrons in the CB (number of electrons per unit energy per unit volume). The area under nE(E) vs. E is the electron concentration in the conduction band.We thus replacing Fermi-Dirac statistics by Boltzmann statistics and inherently as

46、suming that the number of electrons in CB is far less than the number states in this band.3.1.4. Electron and hole concentration(a) Energy band diagram. (b)Density of states (number of states per unit energy per unit volume). (c) Fermi-Dirac probability function (probability of occupancy of a state)

47、. (d) The product of g(E) and f(E) is the energy density of electrons in the CB (number of electrons per unit energy per unit volume). The area under nE(E) vs. E is the electron concentration in the conduction band.3.1.4. Electron and hole concentration(a) Energy band diagram. (b)Density of states (

48、number of states per unit energy per unit volume). (c) Fermi-Dirac probability function (probability of occupancy of a state). (d) The product of g(E) and f(E) is the energy density of electrons in the CB (number of electrons per unit energy per unit volume). The area under nE(E) vs. E is the electron concentration in the conduction band.3.1.4. Electron and hole concentration3.1.4. Electron and hole concentration3.1.4. Electron and hole concentration